# Uniqueness in Rough Almost Complex Structures, and Differential Inequalities

Jean-Pierre Rosay^{[1]}

- [1] University of Wisconsin Department of Mathematics Madison WI 53705 (USA)

Annales de l’institut Fourier (2010)

- Volume: 60, Issue: 6, page 2261-2273
- ISSN: 0373-0956

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topRosay, Jean-Pierre. "Uniqueness in Rough Almost Complex Structures, and Differential Inequalities." Annales de l’institut Fourier 60.6 (2010): 2261-2273. <http://eudml.org/doc/116332>.

@article{Rosay2010,

abstract = {The study of $J$-holomorphic maps leads to the consideration of the inequations $|\frac\{\partial u\}\{\partial \{\overline\{z\}\}\}|\le C|u|$, and $|\frac\{\partial u\}\{\partial \{\overline\{z\}\}\}| \le \epsilon |\frac\{\partial u\}\{\partial z\}|$. The first inequation is fairly easy to use. The second one, that is relevant to the case of rough structures, is more delicate. The case of $u$ vector valued is strikingly different from the scalar valued case. Unique continuation and isolated zeroes are the main topics under study. One of the results is that, in almost complex structures of Hölder class $\frac\{1\}\{2\}$, any $J$-holomorphic curve that is constant on a non-empty open set, is constant. This is in contrast with immediate examples of non-uniqueness.},

affiliation = {University of Wisconsin Department of Mathematics Madison WI 53705 (USA)},

author = {Rosay, Jean-Pierre},

journal = {Annales de l’institut Fourier},

keywords = {$J$-holomorphic curves; differential inequalities; uniqueness; -holomorphic curves},

language = {eng},

number = {6},

pages = {2261-2273},

publisher = {Association des Annales de l’institut Fourier},

title = {Uniqueness in Rough Almost Complex Structures, and Differential Inequalities},

url = {http://eudml.org/doc/116332},

volume = {60},

year = {2010},

}

TY - JOUR

AU - Rosay, Jean-Pierre

TI - Uniqueness in Rough Almost Complex Structures, and Differential Inequalities

JO - Annales de l’institut Fourier

PY - 2010

PB - Association des Annales de l’institut Fourier

VL - 60

IS - 6

SP - 2261

EP - 2273

AB - The study of $J$-holomorphic maps leads to the consideration of the inequations $|\frac{\partial u}{\partial {\overline{z}}}|\le C|u|$, and $|\frac{\partial u}{\partial {\overline{z}}}| \le \epsilon |\frac{\partial u}{\partial z}|$. The first inequation is fairly easy to use. The second one, that is relevant to the case of rough structures, is more delicate. The case of $u$ vector valued is strikingly different from the scalar valued case. Unique continuation and isolated zeroes are the main topics under study. One of the results is that, in almost complex structures of Hölder class $\frac{1}{2}$, any $J$-holomorphic curve that is constant on a non-empty open set, is constant. This is in contrast with immediate examples of non-uniqueness.

LA - eng

KW - $J$-holomorphic curves; differential inequalities; uniqueness; -holomorphic curves

UR - http://eudml.org/doc/116332

ER -

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